A theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors is proved in this paper. The result complements previous work by S.S. Yang (1981) and N. Gribkova and R. Zitikis (2017, 2019). The proof is based on the conditional independence property of the concomitants established by P. K. Bhattacharya (1974); the van Zwet strong law of large numbers for linear functions of order statistics (1980) is used and classical inequalities apply, including the Rosenthal inequality (1970).